Mathematics: Solve 3 log6 2 + 2 log6 3 − log6 x = 2.

Solve 3 log6 2 + 2 log6 3 − log6 x = 2. - id362263622503022, arosh4763

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arieannaensley0616

03.01.2022

$D:x \ \textgreater \ 0\\\\3\log_62+2\log_63-\log_6x=2\\-----------------------\\Use:\\\log_ab=c\iff a^c=b\\\log_ab+\log_ac=\log_a(bc)\\\log_ab-\log_ac=\log_a(\frac{b}{c})\\\log_ab^c=c\log_ab\\-----------------------\\\log_62^3+\log_63^2-\log_6x=2\\\\\log_68+\log_69-\log_6x=\log_66^2\\\\\log_6(8\cdot9)-\log_6x=\log_636\\\\\log_672-\log_6x=\log_636\\\\\log_6\frac{72}{x}=\log_636\iff\dfrac{72}{x}=36\\\\\dfrac{x}{72}=\dfrac{1}{36}\ \ \ \ \ |multiply\ both\ sides\ by\ 72\\\\x=\dfrac{72}{36}\\\\\boxed{x=2}\in D$

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Ответ:

Flameking1223

01.04.2021

Mathematics

Y= 4/5 x + 24
To find the rate of change you find the difference in each of the numbers on the graph. For example, 36-32 is 4. So 28-4 is 24 and that would be the next number down. It would also match x to be 0 because since the rate of change for x was 5, if you subtract 5 from 5 you get 0. So from this we know that the coordinates would be 0,5.
From this info, the slope would be 4/5 and the y intercept or initial value would be 24

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Solve 3 log6 2 + 2 log6 3 − log6 x = 2.

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